Coordinates and Distance Formula

One formula to rule them all, one formula to find them. One formula to bring them all, and in the darkness bind them. Or something like that. In coordinate geometry, the way to find the distance between two points is to use the distance formula. All you do is plug in the points, and you've got yourself the distance.

AlgebraCoordinates and Graphs
Coordinate GeometryDistance Formula
GeometryCoordinate Geometry
Use coordinates to prove simple geometric theorems algebraically
LanguageEnglish Language
Mathematics and Statistics AssessmentPlane Geometry
Plane GeometryPlane figures (triangles, rectangles, parallelograms, trapezoids, circles, polygons)
Properties, Measurement, and DimensionUse coordinates to prove geometric theorems algebraically

Transcript

00:27

Rohan middle-earth center.. Mount Doom is located exactly eight leagues east and

00:33

nine leagues south of Rohan how far do Frodo and his friends have to travel on [Woman standing on a clifftop]

00:38

their quest to destroy the donut rather than use a pedometer to find the

00:44

distance we can make use of coordinates and the distance formula.... let's look at

00:49

middle-earth as a coordinate plane using Rohan as the origin and north, south, east

00:56

and west as our axes we can find the coordinates of Hobbit town and Mount Doom [Rohan and Mount Doom appear on coordinate map]

01:01

Hobbiton is 13 leagues west and 19 leagues north of Rohan

01:06

so it's coordinates are negative 13, 19 Mount Doom is eight leagues east and

01:13

nine leagues south of Rohan so it's coordinates are 8, negative 9.. Now

01:19

that we have the coordinates of our two end points we can calculate the distance [Line between Hobbiton and Mount Doom appears]

01:22

between them using the one formula to rule them all the distance D equals the

01:28

square root of x2 minus x1 squared plus y2 minus y1 squared where x1 y1 and x2

01:37

y2 are the coordinates of the two end points Frodo and his friends start out

01:43

in Hobbiton so that's our first point x1 equals negative 13 and y1 equals 19

01:50

they want to get to the other end point Mount Doom so x2 equals 8 and y2 equals [Distance formula appears]

01:56

negative 9 if we plug these numbers into our formula we should get D equals the

02:02

square root of 8 minus negative 13 squared plus negative 9 minus 19 squared

02:09

simplifying that all the way will get us D equals 35... so the distance from Hobbiton

02:16

to Mount Doom is exactly 35 leagues how long that'll take [Man checks watch]

02:20

well that's a different matter [Gollum hops along]